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This means that:^^^^^
((k'_1)^2 + (k''_2)^2)/(n_1)^2 = ((k'_2)^2 + (k''_2)^2)/(n_2)^2 . ...
Suppose that n_1 > n_2 so that the wave is going from a lower index region
(1) into a higher index region (2). In this case ....
Suppose that n_1 > n_2 so that the wave is going from a HIGHER index region
(1) into a LOWER index region (2). In this case ....